When I work out, I like to incorporate a variety of training techniques into my programs to improve my power, strength, and speed. The strength exercise I've been really into lately is the suitcase deadlift.
I like it because deadlifts are great for lower-body strength, back strength, and power. Add in the unilateral exercise (an exercise focusing on one side of the body), and in my opinion, it becomes even better as you're forced to address imbalances and strengthen both sides of the body. Then you overload one side of your body, aka you add weight/resistance, and boom, your core has no choice but to be involved. You can do this move with a barbell if you're more advanced, but if not, a kettlebell will suffice.
If you want a stronger core and legs, definitely program this exercise into your workouts.
Before getting started, warm up your muscles with a few glute activation and core activation exercises.